select the correct answer.

the variable $b$ varies directly as the square root of $c$. if $b = 100$ when $c = 4$, which equation can be used to find other combinations of $b$ and $c$?

$b = 200c$
$b = 25c$
$b\sqrt{c} = 50$
$b = 50\sqrt{c}$

Question

select the correct answer.

the variable $b$ varies directly as the square root of $c$. if $b = 100$ when $c = 4$, which equation can be used to find other combinations of $b$ and $c$?

$b = 200c$
$b = 25c$
$b\sqrt{c} = 50$
$b = 50\sqrt{c}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Constant of Variation" ], "new_concepts": [ "Direct Variation" ], "current_concepts": [ "Direct Variation", "Constant of Variation" ] } ## Set up the direct variation equation $$ b = k\sqrt{c} $$ ## Solve for the constant of variation $$ \begin{aligned} 100 &= k\sqrt{4} \ 100 &= 2k \ k &= 50 \end{aligned} $$ ## Write the final equation $$ b = 50\sqrt{c} $$

(A) $b = 200c$

(B) $b = 25c$

(C) $b\sqrt{c} = 50$

(D) $b = 50\sqrt{c}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the direct variation equation

Solve for the constant of variation

Write the final equation

Answer: